Doing something one time is not going to produce a cure to your issue. You should go see a PT and get the issue figured out and fixed not chase your tail with internet advice.
Fix it before it gets worse. Iāve had shoulder issues. They suck.
Wearing the backpack can make you shrug your traps and elevate your shoulders. Itās possible to get ātrap dominantā and overdo the shrug/elevating or up and down motion.
When you plank your shoulder is supposed to move forward, around your ribs. If your trap is over-working, your shoulder goes āupā instead of āforwardā when you get in the plank position. This crunches everything up and causes pain.
When you do the DB external rotation seated or standing you do more of that elevating, āupā motion and work the muscles on ātopā of your shoulder. So it makes sense it didnāt help much.
Try the side lying external rotation to work the muscles that keep your shoulder ādown.ā
I donāt know what the rest of your program looks like, but the Landmine Press is another good move to train the āfront to backā motion of your shoulder while you press.